Final Report

THERMO ELASTIC AND STRESS ANALYSIS OF

DISC BRAKE

A PROJECT REPORT

Submitted by

ELANGO.N (090111139011)

VIGNESHKUMARAN.C (090111139053)

ARAVINDKUMAR.N (100411139001)

In partial fulfillment for the award of degree

of

BACHELOR OF ENGINEERING

in

MECHANICAL ENGINEERING

P.A. COLLEGE OF ENGINEERING AND TECHNOLOGY, POLLACHI.

ANNA UNIVERSITY, CHENNAI – 600 025

APRIL 2012

ii

ANNA UNIVERSITY, CHENNAI – 600 025

BONAFIDE CERTIFICATE

Certified that this project report “THERMO ELASTIC AND STRESS

ANALYSIS OF DISC BRAKE” is the bonafide work of N. ELANGO

(09011139011), C.VIGNESHKUMARAN(09011139053), N.ARAVINDKUMAR

(100411139001) who carried out the project work under my supervision.

SIGNATURE SIGNATURE

SUPERVISOR HEAD OF THE DEPARTMENT

Prof. T. VARUNKUMAR Dr. V. RAMALINGHAM

Assistant professor, Dean / Head of the department,

Department of Mechanical Engg., Department of Mechanical Engg,

P.A. College of Engg. & Technology, P.A. College of Engg. & Technology,

Pollachi – 642002. Pollachi – 642002.

iii

ACKNOWLEDGEMENT

Our sincere thanks to our respected chairman and chairperson for their

encouragement towards our project activities and providing necessary accessories.

We express our sincere gratitude to Dr.T.Manikandan, Principal and

Dr.V.Ramalingam, Dean cum Head of Department, Department of Mechanical

Engineering, P.A College of Engineering and Technology, Pollachi for providing

the available resources in the college.

We have a great pleasure in expressing our sincere gratitude for the valuable

suggestions to our guide Mr. T. Varunkumar, Assistant Professor of Mechanical

Engineering. Our special thanks to Mr. N. Manikandan, Mechanical Department

for the valuable suggestions in completing the project successfully.

We would like to thank all our staff members and lab technicians for giving

valuable guidance to our project. Our special thanks to our classmates for their

enthusiastic attitude and calming influence.

iv

CONTENTS

CH. NO TITLE PAGE NO

Acknowledgement iii

List of figures vi

List of table vii

Abstract viii

1 INTRODUCTION 1 - 4

1.1 Introduction 1

1.2 Classification 1

1.3 Disc brake 2

1.3.1 Floating Caliper Type 3

1.3.2 Fixed Caliper Type 3

1.4 Problems in Disc brake 4

1.5 Objective of the present Study 4

2 LITERATURE REVIEW 5 - 7

3 FINITE ELEMENT ANALYSIS 8 - 15

3.1 Introduction 8

3.2 Procedure for ANSYS analysis 8

3.2.1 Build the model 9

3.2.2 Material Properties 9

3.2.3 Solution 9

a. Pre processor 9

b. Element Type 10

c. Homogeneous structure 11

d. Layered structure solid 11

e. Geometric Definition 11

v

f. Model Generation 11

g. Mesh Generation 11

h. Finite Element Generation 12

i. Boundary conditions & loading 12

j. Model display 12

k. Material defection 12

l. Solution 13

m. Post processor 13

3.3 Thermal analysis 14

3.3.1 Types of thermal Analysis 14

3.3.2 Planning the Analysis 14

3.4 Structural analysis 14

3.4.1 Types of thermal Analysis 15

3.4.2 Planning the Analysis 15

4 MODELING AND ANALYSIS 16 - 20

4.1 Definition of problem domain 17

4.2 Dimension of disc brake 17

4.3 Finite element mesh 18

4.4 Solution 20

5 RESULT AND DISCUSSION 21 - 23

5.1 Validation of result 21

5.2 Materials analyzed 21

5.2.1 Cast iron 21

5.2.2 Stainless Steel 22

5.2.3 Alumina 22

5.2.4 E-Glass Fiber 23

6 CONCLUSION 30 - 33

7 REFERENCES 34

vi

LIST OF FIGURES AND TABLES

LIST OF FIGURES

FIG. NO DESCRIPTION PAGE NO

1.1 Disc brake assembly 2

1.2 Floating caliper disc brake 3

1.3 Fixed caliper disc brake 3

4.1 Dimensions of disc brake model 17

4.2 Imported model of disc 18

4.3 Meshed model 19

4.4 Loaded model of the disc brake 19

5.1 Von Mises stress distribution in cast iron disk 24

5.2 Von Mises stress distribution in stainless steel disk 24

5.3 Von Mises stress distribution in alumina disk 25

5.4 Von Mises stress distribution E-glass fiber disk 25

5.5 Elastic strain in cast iron disk 26

5.6 Elastic strain in stainless steel disk 26

5.7 Elastic strain in alumina disk 27

5.8 Elastic strain in E-glass fiber disk 27

5.9 Average displacement in cast iron disk 28

5.10 Average displacement in stainless steel disk 28

5.11 Average displacement in alumina disk 29

5.12 Average displacement in E-glass fiber disk 29

6.1 Graph – Comparison for stress values 31

6.2 Graph – Comparison for strain values 31

6.3 Graph – Comparison for displacement values 32

vii

LIST OF TABLES

TABLE NO DESCRIPTION PAGE NO

3.1 Steps used in ANSYS 10

5.1 Material properties of Cast iron 22

5.2 Material properties of Stainless Steel 22

5.3 Material properties of Alumina 23

5.4 Material properties of E- Glass fiber 23

5.5 Comparison 32

viii

ABSTRACT

Transient Thermal and Structural Analysis of the Rotor Disc of Disk Brake is

aimed at evaluating the performance of disc brake rotor of a car under severe braking

conditions and there by assist in disc rotor design and analysis. An investigation into

usage of new materials is required which improve braking efficiency and provide greater

stability to vehicle. This investigation can be done using ANSYS software. ANSYS 13.0

is a dedicated finite element package used for determining the temperature distribution,

variation of the stresses and deformation across the disc brake profile. In the present

work, an attempt has been made to investigate the suitable hybrid aluminum based

material which is lighter than stainless steel and has good Young’s modulus, Yield

strength and density properties. Aluminum base metal matrix composite have a promising

friction and wear behavior as a Disk brake rotor. The transient thermo elastic analysis of

Disc brakes in severe braking condition has been performed and the results were going to

be compared. And also thermo elastic instability (TIE) phenomenon (the unstable growth

of contact pressure) is going to be investigated in the present study, and the influence of

the material properties on the thermo elastic behaviors (the maximum temperature on the

friction surfaces) is calculated to facilitate the conceptual design of the disk brake

system. By identifying the true design features, the extended service life and long term

stability is assured.

1

CHAPTER -1

INTRODUCTION

1.1 INTRODUCTIONA brake is a device by means of which artificial frictional resistance is applied to

moving machine member, in order to stop the motion of a machine.

In the process of performing this function, the brakes absorb either kinetic energy of

the moving member or the potential energy given up by objects being lowered by hoists,

elevators etc. The energy absorbed by brakes is dissipated in the form of heat. This heat is

dissipated in the surrounding atmosphere to stop the vehicle, so the brake system should have

following requirements:

The brakes must be strong enough to stop the vehicle with in a minimum distance in an

emergency.

The driver must have proper control over the vehicle during braking and vehicle must

not skid.

The brakes must have well anti fade characteristics i.e. their effectiveness should not

decrease with constant prolonged application.

The brakes should have anti wear properties.

1.2 CLASSIFICATIONThe mechanical brakes according to the direction of acting force may be divided into

the following two groups:

Radial Brake

Axial Brake

Radial brakes

In these brakes the force acting on the brakes drum is in radial direction. The radial

brakes may be subdivided into external brakes and internal brakes.

Axial Brakes

In these brakes the force acting on the brake drum is only in the axial direction. i.e.

Disk brakes, Cone brakes.

2

1.3 DISK BRAKEA disk brake consists of a stainless steel disk bolted to the wheel hub and a stationary

housing called caliper. The caliper is connected to some stationary part of the vehicle like

the axle casing or the stub axle as is cast in two parts each part containing a piston.

In between each piston and the disk there is a friction pad held in position by retaining

pins, spring plates etc. passages are drilled in the caliper for the fluid to enter or leave

each housing. The passages are also connected to another one for bleeding. Each cylinder

contains rubber-sealing ring between the cylinder and piston. A schematic diagram is shown

in the figure 1.1.

Figure 1.1 Disc Brake Assembly

The main components of the disc brake are:

The Brake Pads

The Caliper which contains the piston

The Rotor, which is mounted to the hub

When the brakes are applied, hydraulically actuated pistons move the friction pads in

to contact with the rotating disk, applying equal and opposite forces on the disk. Due to the

friction in between disk and pad surfaces, the kinetic energy of the rotating wheel is

converted into heat, and stop after a certain distance. On releasing the brakes the brakes the

rubber-sealing ring acts as return spring and retract the pistons and the friction pads away from

the disk.

3

1.3.1 Floating Caliper TypeThe floating caliper design is not only more economical and lighter weight but also

requires fewer parts than its fixed caliper counterpart. Depending on the application, the

floating caliper has either one or two pistons.

Figure 1.2 Floating Caliper Disc Brake

The piston is located in one side of the caliper only. Hydraulic pressure from the

master cylinder is applied to piston (A) and thus presses the inner pad against the disc rotor.

At the same time, an equal hydraulic pressure (reaction force B) acts on the bottom of the

cylinder. This causes the caliper to move to the right, and presses the outer pad located

opposite the piston against the disc rotor. The piston exerts pressure on the inside pad as well

as moving the caliper body to engage the outside pad.

1.3.2 Fixed Caliper Type

Figure 1.3 Fixed Caliper Disc Brake

The fixed caliper design has pistons located on both sides of the caliper providing equal

force to each pad. The caliper configuration can incorporate one or two pistons on each side.

4

The ability to include multiple pistons provides for greater braking force and a compact design.

Because these assemblies are larger and heavier than the floating caliper, they absorb

and dissipate more heat. This design is able to withstand a greater number of repeated hard

stops without brake fade. This design is found on models which include larger engine

displacement such as the V-6 Camry and Avalon as well as the Supra and four-wheel-drive

Truck, T100 and Tacoma.

1.4 PROBLEMS IN DISK BRAKEIn the course of brake operation, frictional heat is dissipated mostly into pads and a disk,

and an occasional uneven temperature distribution on the components could induce

severe thermo elastic distortion of the disk. The thermal distortion of a normally flat surface

into a highly deformed state, called thermo elastic transition. At other times, however, the

stable evolution behavior of the sliding system crosses a threshold whereupon a sudden

change of contact conditions occurs as the result of instability.

This invokes a feedback loop that comprises the localized elevation of frictional

heating, the resultant localized bulging, a localized pressure increases as the result of

bulging, and further elevation of frictional heating as the result of the pressure increase.

When this process leads to an accelerated change of contact pressure distribution, the

unexpected hot roughness of thermal distortion may grow unstably under some

conditions, resulting in local hot spots and leaving thermal cracks on the disk. This is known

as thermo elastic instability (TEI).

The thermo elastic instability phenomenon occurs more easily as the rotating speed

of the disk increases. This region where the contact load is concentrated reaches very high

temperatures, which cause deterioration in braking performance. Moreover, in the course of

their presence on the disk, the passage of thermally distorted hot spots moving under the

brake pads causes low-frequency brake vibration.

1.5 OBJECTIVE OF THE PRESENT STUDYThe present investigation is aimed to study:

The given disk brake rotor of its stability and rigidity (for this Thermal analysis

and coupled structural analysis is carried out on a given disk brake rotor.

Best combination of parameters of disk brake rotor like Flange width, Wall

thickness and material there by a best combination is suggested.

5

CHAPTER - 2

LITERATURE REVIEW

In order to study the transient thermo elastic behavior of the disk brake , the literature

related to the thermo elastic analysis of clutch, two sliding surfaces and brakes have been

studied. Since in the past most of the studies of brake and clutch is carried out for thermo

elastic analysis by considering it as a case of two dimensional. The following section details

the literature available and relevant to the proposed study of transient thermo elastic analysis

of a solid disk brake, as a case of three dimensional.

F.E. Kennedy et al [1] developed the numerical and experimental methods applied to

tribology. He improved the techniques for finite element analysis of sliding surface temperature.

Essential component of manually operated vehicle transmission is the synchronizer.

Synchronizers have the task of minimizing the speed difference between the shifted gearwheel

and the shaft by means of frictional torque before engaging the gear. Proper operation

requires a sufficiently high coefficient of friction. It is common practice to investigate the

friction and wear behavior under various loading conditions on test rigs or in vehicle tests. An

optimized design of the system with regard to appropriate function and durability on the one

hand as well as low cost, low mass and compact overall dimensions on the other hand requires

extensive testing. According to the present state of knowledge, derived from numerous

experimental investigations, temperature can be attributed the most significant influence on

the tribology of synchronizing systems. Therefore, the influence of various loading

conditions on contact temperature was investigated; a relation between temperature

and tribological performance was established. The Finite Element Method was applied to

simulate the thermal behavior of a synchronizing system depending on different operating

conditions. Characteristics o f t h e tribological performance of the molybdenum coated

synchromesh ring in contact with a steel cone were derived from extensive experimental

investigations. Significantly different friction and wear patterns can be distinguished. At heavy

loading conditions the coefficient of friction is quite high and continuously severe wear

occurs; light operating conditions results in a low friction coefficient, whilst no more wear is

observed. Between those two extremes an indifferent regime exists, in which both patterns of

tribological behavior occur.

A reason for this characteristics behavior of the system described here was found by

means of the Finite Element simulation. Apparently, the friction and wear pattern

6

depends on the temperature in the contact area; for mild wear and the low friction

co efficient the contact temperature must not exceed a critical value in order to avoid severe

wear. Within limits the predicted tribological behavior and the test results are in good

agreement. The calculation of the temperature in the contact area provides a basis for a

classification of the load conditions in terms of their thermal and tribological effect, a

practically applicable estimation of service life and a design procedure based on

numerical simulation rather than on testing.

J.Y.Lin et al Radial transient heat conduction in composite hollow cylinders with the

temperature-dependent thermal conductivity was investigated numerically by using an

application of the Laplace transform technique combined with the finite element method

(FEM) or with the finite difference method (FDM). The domain of the governing equation

was discretized using the FEM or FDM. The nonlinear terms were linear zed by Taylor's series

approximation. The time-derivatives in the linear zed equations were transformed to the

corresponding algebraic terms by the application of the Laplace transform. The numerical

inversion of the Laplace transform was applied to invert the transformed temperatures to the

temperatures in the physical quantity. Since the present method was not a time-stepping

procedure, the results at a specific time can be calculated in the time domain without any step-

by-step computations. To show the accuracy of the present method for the problems under

consideration, a comparison of the hybrid finite element solutions with the hybrid finite

difference solutions was made.

J. Brilla et al [3] generalized variational principles in the sense of the Laplace

transform for viscoelasti problems were derived. Then mathematical theory of viscoelasticity

in generalized Hardy spaces and in weighted anisotropic Sobolevspaces and spectral theory of

corresponding non-self adjoint operators was elaborated. Finally the Laplace transform FEM for

numerical analysis of time-dependent problems of the mathematical physics was proposed and

analyzed.

S. V. Tsinopoulos et al [4] an advanced boundary element method was appropriately

combined with the fast Fourier transform (FFT) to analyze general axisymmetric

problems in frequency domain elastodynamics. The problems were characterized by

axisymmetric geometry and non-axisymmetric boundary conditions. Boundary quantities were

expanded in complex Fourier series in the circumferential direction and the problem was

7

efficiently decomposed into a series of problems, which were solved by the BEM for the

Fourier boundary quantities, discretizing the surface generator of the axisymmetric body.

Quadratic boundary elements were used and BEM integrations were done by FFT

algorithm in the circumferential direction and by Gauss quadrature in the generator direction.

Singular integrals were evaluated directly in a highly accurate way. The Fourier transformed

solution was then numerically inverted by the FFT provided the final solut ion . The method

combines high accuracy and efficiency and this was demonstrated illustrative numerical

examples.

H. C. Wang et al [5] a new numerical method was proposed for the boundary element

analysis of axisymmetric bodies. The method was based on complex Fourier series

expansion of boundary quantities in circumferential direction, which reduces the

boundary element equation to an integral equation in (r-z) plane involving the Fourier

coefficients of boundary quantities, where r and z are the co-ordinates of the (r, ө, z)

cylindrical co-ordinate system. The kernels appearing in these integral equations can be

computed effectively by discrete Fourier transform formulas together with the fast

Fourier transform (FFT) algorithm, and the integral equations in (r-z) plane can be solved by

Gaussian quadrature, which establishes the Fourier coefficients associated with boundary

quantities. The Fourier transform solution can then be inverted into (r, ө, and z) space by using

again discrete Fourier transform formulas together with FFT algorithm. In the study, first we

presented the formulation of the proposed method which was outlined above. Then, the method

was assessed by using three sample problems. A good agreement was observed in the

comparisons of the predictions of the method with those available in the literature. It was

further found that the proposed method provided considerable saving in computer time

compared to existing methods.

8

CHAPTER -3

FINITE ELEMENT ANALYSIS

3.1 INTRODUCTION

The finite element method is numerical analysis technique for obtaining approximate

solutions to a wide variety of engineering problems. Because of its diversity and flexibility as

an analysis tool, it is receiving much attention in almost every industry. In more and more

engineering situations today, we find that it is necessary to obtain approximate solutions

to problem rather than exact closed form solution.

It is not possible to obtain analytical mathematical solutions for many engineering

problems. An analytical solutions is a mathematical expression that gives the values of the

desired unknown quantity at any location in the body, as consequence it is valid for infinite

number of location in the body. For problems involving complex material properties and

boundary conditions, the engineer resorts to numerical methods that provide approximate,

but acceptable solutions.

The finite element method has become a powerful tool for the numerical solutions of a

wide range of engineering problems. It has been developed simultaneously with the increasing

use of the high- speed electronic digital computers and with the growing emphasis on

numerical methods for engineering analysis. This method started as a generalization of the

structural idea to some problems of elastic continuum problem, started in terms of different

equations.

3.2 PROCEDURE FOR ANSYS ANALYSISStatic analysis is used to determine the displacements stresses, stains and forces in

structures or components due to loads that do not induce significant inertia and damping

effects. Steady loading in response conditions are assumed. The kinds of loading that can

be applied in a static analysis include externally applied forces and pressures, steady state

inertial forces such as gravity or rotational velocity imposed (non-zero)

displacements, temperatures (for thermal strain).

A static analysis can be either linear or non linear. In our present work we

consider linear static analysis.

9

The procedure for static analysis consists of these main steps

Building the model

Obtaining the solution

Reviewing the results.

3.2.1 BUILD THE MODELIn this step we specify the job name and analysis title use PREP7 to define the

element types, element real constants, material properties and model geometry element type

both linear and nonlinear structural elements are allowed. The ANSYS elements library

contains over 80 different element types. A unique number and prefix identify each element

type.

E.g. BEAM 94, PLANE 71, SOLID 96 and PIPE 16

3.2.2 MATERIAL PROPERTIESYoung’s modulus (EX) must be defined for a static analysis. If we plan to apply

inertia loads (such as gravity) we define mass properties such as density (DENS). Similarly

if we plan to apply thermal loads (temperatures) we define coefficient of thermal expansion

(ALPX).

3.2.3 SOLUTIONIn this step we define the analysis type and options, apply loads and initiate the finite

element solution. This involves three phases:

Pre-processor phase

Solution phase

Post-processor phase

a. Pre-processor

Pre processor has been developed so that the same program is available on micro,

mini, super-mini and mainframe computer system. This slows easy transfer of models one

system to other.

10

Table 3.1 Steps used in ANSYS

PREPROCESSOR

PHASESOLUTION PHASE

POST-PROCESSOR

PHASE

GEOMETRY

DEFINITONS

ELEMENTMATRIX

FORMULATION

POST SOLUTION

OPERATIONS

MESH

GENERATION

OVERALL MATRIX

TRIANGULARIZATION

POST DATA PRINT

OUT (FOR REPORTS)

MATERIAL (WAVE FRONT) POST DATA

DEFINITIONSSCANNING POST DATA

DISPLAY

CONSTRAINT

DEFINITIONS

DISPLACEMENT,

STRESS, ETC.

LOAD DEFINITION CALCULATION

MODEL DISPLAY

Pre processor is an interactive model builder to prepare the FE (finite element)

model and input data. The solution phase utilizes the input data developed by the pre

processor, and prepares the solution according to the problem definition. It creates input files

to the temperature etc. on the screen in the form of contours.

b. Element type

SOLID185 is used for 3-D modeling of solid structures. It is defined by eight nodes

having three degrees of freedom at each node: translations in the nodal x, y, and z directions.

The element has plasticity, hyper elasticity, stress stiffening, creep, large deflection, and large

strain capabilities. It also has mixed formulation capability for simulating deformations of

nearly incompressible elasto plastic materials, and fully incompressible hyper elastic materials.

SOLID185 is available in two forms:

Homogeneous Structural Solid (KEYOPT(3) = 0, the default)

Layered Structural Solid (KEYOPT(3) = 1)

11

c. Homogeneous Structure

SOLID185 Structural Solid is suitable for modeling general 3-D solid structures. It

allows for prism and tetrahedral degenerations when used in irregular regions. Various element

technologies such as B-bar, uniformly reduced integration, and enhanced strains are supported.

d. Layered structure solid

SOLID185 Layered Solid to model layered thick shells or solids. The layered section

definition is given by ANSYS section (SECxxx) commands. A prism degeneration option is also

available.

e. Geometric Definitions

There are four different geometric entities in pre processor namely key points, lines,

area and volumes. These entities can be used to obtain the geometric representation of the

structure. All the entities are independent of other and have unique identification labels.

f. Model Generations

Two different methods are used to generate a model:

Direct generation.

Solid modeling

With solid modeling we can describe the geometric boundaries of the model,

establish controls over the size and desired shape of the elements and then instruct

ANSYS program to generate all the nodes and elements automatically. Although, some

automatic data generation is possible (by using commands such as FILL, NGEN, EGEN etc)

the direct generation method essentially a hands on numerical method that requires us to

keep track of all the node numbers as we develop the finite element mesh. This detailed

book keeping can become difficult for large models, giving scope for modeling errors. Solid

modeling is usually more powerful and versatile than direct generation and is commonly

preferred method of generating a model.

g. Mesh generation

In the finite element analysis the basic concept is to analyze the structure, which is an

assemblage of discrete pieces called elements, which are connected, together at a finite

number of points called Nodes. Loading boundary conditions are then applied to these

elements and nodes. A network of these elements is known as Mesh.

12

h. Finite element generation

The maximum amount of time in a finite element analysis is spent on generating

elements and nodal data. Preprocessor allows the user to generate nodes and elements

automatically at the same time allowing control over size and number of elements. There are

various types of elements that can be mapped or generated on various geometric entities.

The elements developed by various automatic element generation capabilities of pre

processor can be checked element characteristics that may need to be verified before the finite

element analysis for connectivity, distortion-index etc.

Generally, automatic mesh generating capabilities of pre processor are used rather than

defining the nodes individually. If required nodes can be defined easily by defining the

allocations or by translating the existing nodes. Also on one can plot, delete, or search nodes.

i. Boundary conditions and loading

After completion of the finite element model it has to constrain and load has to be applied

to the model. User can define constraints and loads in various ways. All constraints and loads

are assigned set ID. This helps the user to keep track of load cases.

j. Model display

During the construction and verification stages of the model it may be necessary to view

it from different angles. It is useful to rotate the model with respect to the global system and

view it from different angles. Pre processor offers these capabilities. By windowing feature

pre processor allows the user to enlarge a specific area of the model for clarity and details.

Pre processor also provides features like smoothness, scaling, regions, active set, etc for

efficient model viewing and editing.

k. Material defections

All elements are defined by nodes, which have only their location defined. In the case of

plate and shell elements there is no indication of thickness. This thickness can be given as

element property. Property tables for a particular property set 1-D have to be input.

Different types of elements have different properties for e.g.

Beams : Cross sectional area, moment of inertia etc

Shell : Thickness

Springs : Stiffness

Solids : None

13

The user also needs to define material properties of the elements. For linear static

analysis, modules of elasticity and Poisson’s ratio need to be provided. For heat transfer,

coefficient of thermal expansion, densities etc. are required. They can be given to the

elements by the material property set to 1-D.

l. Solution

The solution phase deals with the solution of the problem according to the problem

definitions. All the tedious work of formulating and assembling of matrices are done by the

computer and finally displacements are stress values are given as output. Some of the

capabilities of the ANSYS are linear static analysis, non linear static analysis, transient

dynamic analysis, etc.

m. Post- processor

It is a powerful user-friendly post-processing program using interactive color graphics.

It has extensive plotting features for displaying the results obtained from the finite element

analysis. One picture of the analysis results (i.e. the results in a visual form) can often

reveal in seconds what would take an engineer hour to assess from a numerical output,

say in tabular form. The engineer may also see the important aspects of the results that could

be easily missed in a stack of numerical data.

Employing state of art image enhancement techniques, facilities viewing of:

Contours of stresses, displacements, temperatures, etc.

Deform geometric plots

Animated deformed shapes

Time-history plots

Solid sectioning

Hidden line plot

Light source shaded plot

Boundary line plot etc.

The entire range of post processing options of different types of analysis can be

14

accessed through the command/menu mode there by giving the user added flexibility and

convenience.

3.3 THERMAL ANALYSIS

A thermal analysis calculates the temperature distribution and related thermal

quantities in brake disk. Typical thermal quantities are:

1. The temperature distribution

2. The amount of heat lost or gained

3. Thermal fluxes

3.3.1 Types of thermal analysis

1. A steady state thermal analysis determines the temperature

distribution and other thermal quantities under steady state loading

conditions. A steady state loading condition is a situation where heat

storage effects varying over a period of time can be ignored.

2. A transient thermal analysis determines the temperature distribution and

other thermal quantities under conditions that varying over a period of

time.

3.3.2 Planning the analysis

In this step a compromise between the computer time and accuracy of the analysis is

made. The various parameters set in analysis are given below:

Thermal modeling

Analysis type? Thermal h-method.

Steady state or Transient? Transient

Thermal or Structural? Thermal

Properties of the material? Isotropic

Objective of analysis- to find out the stress distribution in the brake disk when the

process of braking is done.

Units – SI

3.4 STRUCTURAL ANALYSISStructural analysis is the most common application of the finite element analysis. The

term structural implies civil engineering structure such as bridge and building, but also

naval, aeronautical and mechanical structure such as ship hulls, aircraft bodies and

15

machine housing as well as mechanical components such as piston, machine parts and tools.

3.4.1 Types of structural analysis

The seven types of structural analyses in ANSYS. One can perform the following

types of structural analysis. Each of these analysis types are discussed as follows:

Static analysis

Modal analysis

Harmonic analysis

Transient dynamic analysis

Spectrum analysis

Buckling analysis

Explicit dynamic analysis

3.4.2 Structural static analysis

A static analysis calculates the effects of steady loading conditions on a structure,

while ignoring inertia and damping effects such as those caused by time varying loads. A static

analysis can, however include steady inertia loads (such as gravity and rotational velocity),

and time varying loads that can be approximately as static equivalent loads (such as static

equivalent wind and seismic loads).

16

CHAPTER - 4

MODELING AND ANALYSIS

It is very difficult to exactly model the brake disk, in which there are

still researches are going on to find out transient thermo elastic behavior of disk brake

during braking applications. There is always a need of some assumptions to model any

complex geometry. These assumptions are made, keeping in mind the difficulties

involved in the theoretical calculation and the importance of the parameters that

are taken and those which are ignored. In modeling we always ignore the things

that are of less importance and have little impact on the analysis. The assumptions are made

depending upon the details and accuracy required in modeling.

The assumptions which are made while modeling the process are given below:-

1. The disk material is considered as homogeneous and isotropic.

2. The domain is considered as axis-symmetric.

3. Inertia and body force effects are negligible during the analysis.

4. The disk is stress free before the application of brake.

5. Brakes are applied on the front wheel.

6. The analysis is based on pure thermal loading and vibration and thus

only stress level due to the above said is done. The analysis does not

determine the life of the disk brake.

7. Only ambient air-cooling is taken into account and no forced

Convection is taken.

8. The kinetic energy of the vehicle is lost through the brake disks i.e. no

heat loss between the tyre and the road surface and deceleration is

uniform.

9. The disk brake model used is of solid type and not ventilated one.

10. The thermal conductivity of the material used for the analysis is

uniform throughout.

11. The specific heat of the material used is constant throughout and does not

change with temperature.

17

4.1 DEFINITION OF PROBLEM DOMAIN

Due to the application of brakes on the disk brake rotor, heat generation takes

place due to friction and this thermal flux has to be conducted and dispersed

across the disk rotor cross section. The condition of braking is very much severe and

thus the thermal analysis has to be carried out. The thermal loading as well as structure

is axis-symmetric. Hence axis-symmetric analysis can be performed, but in this study

we performed 3-D analysis, which is an exact representation for this thermal analysis.

Thermal analysis is carried out and with the above load structural analysis performed for for

analyzing the stability of the structure.

4.2 DIMENSIONS OF DISK BRAKE

The dimensions of brake disk used for transient thermal and static

structural analysis are shown in Figure. 4.1

Figure 4.1 Dimensions of Disc brakes

18

The models of the disc brakes are developed using the other modeling software’s like Pro/E

Wildfire 5.0.The imported models of the disc brakes are shown in the Figure 4.2.

Figure 4.2 Imported model of Disc brake

4.3 FINITE ELEMENT MESHAccording to given specifications the element type chosen is solid 185.Solid 185 is

higher order version of the 3-D eight node thermal element. The element has 20 nodes with

single degree of freedom, temperature, at each node. The 20-node elements have compatible

temperature shape and are well suited to model curved boundaries.

The 20-node thermal element is applicable to a 3-D, steady state or transient thermal

analysis. If the model containing this element is also to be analyzed structurally, the element

should be replaced by the equivalent structural element.

19

Figure 4.3 Meshed model of the Disc brake

Figure 4.4 Loaded model of the disk brake

20

4.4 SOLUTION

In the solution procedure, frontal solver is used. It involves

After the applying the loads at the respective regions the deformations of the disc

brake is obtained.

The solved solutions are saved in the format of .db file.

The report generated in the solution are taken as the images.

21

CHAPTER - 5

RESULTS AND DISCUSSION

5.1 VALIDATION OF RESULTSFirst of all, to validate the present method, a comparison of transient results with

the steady state solution of thermo elastic behaviors was performed for the operation

condition of the constant hydraulic pressure P =3.006Mpa and angular velocity = 50 rad/s (

drag brake application) during 4.29 seconds. If the transient solution for this operation

condition converges to the steady solution as time elapse, it can be regarded as validation of

the applied transient scheme. The thermal boundary conditions used are adiabatic on the

boundary of the inner and outer radius and the prescribed temperature condition T = 27°C

on the both boundaries along the radius of the lower and upper pad by assumption of

the cooling state. The material properties and operation conditions used for the validation of

the transient thermo elastic scheme are given in Table No -5.1 & 5.2. The time step ∆t =0005

sec. was used.

5.2 MATERIALS ANALYZEDThe various materials were analyzed in this work to get reasonable merits and demerits

of them in the field of braking system. The materials properties are taken for the analysis

purpose in this work. The various materials taken for work are,

Cast iron

Stainless steel

Alumina

E- Glass fiber

5.2.1 CAST IRON

Cast iron is derived from pig iron, and while it usually refers to gray iron, it also

identifies a large group of ferrous alloys which solidify with aeutectic. The color of a fractured

surface can be used to identify an alloy. White cast iron is named after its white surface when

fractured, due to its carbide impurities which allow cracks to pass straight through. Grey cast

iron is named after its grey fractured surface, which occurs because the graphitic flakes deflect

a passing crack and initiate countless new cracks as the material breaks.

22

Table 5.1 Material properties of Cast iron

Material Properties Disk

Thermal conductivity, K (w/m k) 57

Density, ( kg/m3) 7100

Specific heat , c (J/Kg k) 452

Poisson’s ratio, v 0.25

Thermal expansion , · (106 / k ) 11

Elastic modulus, E (GPa) 106

5.2.2 STAINLESS STEEL

In metallurgy, stainless steel, also known as inox steel or inox from French "inoxydable",

is defined as a steel alloy with a minimum of 10.5 or 11% chromium content by mass.

Stainless steel does not corrode, rust or stain with water as ordinary steel does, but despite

the name it is not fully stain-proof. It is also called corrosion-resistant steel or CRES when the

alloy type and grade are not detailed, particularly in the aviation industry. There are different

grades and surface finishes of stainless steel to suit the environment the alloy must endure.

Stainless steel is used where both the properties of steel and resistance to corrosion are required.

Table 5.2 Material properties of Stainless Steel


Thermal conductivity, K (w/m k) 17.2


Specific heat , c(J/Kg k) 500


Thermal expansion , · (106 / k ) 16

Elastic modulus, E(GPa) 190

5.2.3 ALUMINA

Aluminium oxide is an amphoteric oxide with the chemical formula Al2O3. It is

commonly referred to as alumina (α-alumina), or corundum in its crystalline form, as well as

many other names, reflecting its widespread occurrence in nature and industry. Its most

23

significant use is in the production of aluminium metal, although it is also used as an abrasive

owing to its hardness and as a refractorymaterial owing to its high melting point.

Table 5.3 Material properties of Alumina






Thermal expansion , · (106 / k ) 8.6


5.2.4 E-GLASS FIBER

E-Glass or electrical grade glass was originally developed for standoff insulators for electrical

wiring. It was later found to have excellent fiber forming capabilities and is now used almost

exclusively as the reinforcing phase in the material commonly known as fiber glass.

Table 5.4 Material properties of E-Glass Fiber






Thermal expansion , · (106 / k ) 5.4


24

Figure 5.1 Von Mises Stress distribution in Cast Iron

Figure 5.2 Von Mises Stress distribution in Stainless Steel

25

Figure 5.3 Von Mises Stress distribution in Alumina

Figure 5.4 Von Mises Stress distribution in E- Glass fiber

26

Figure 5.5 Elastic Strain distribution in Cast Iron

Figure 5.6 Elastic Strain distribution in Stainless Steel

27

Figure 5.7 Elastic Strain distribution in Alumina

Figure 5.8 Elastic Strain distribution in E- Glass fiber

28

Figure 5.9 Average displacement in Cast Iron

Figure 5.10 Average displacement in Stainless Steel

29

Figure 5.11 Average displacement in Alumina

Figure 5.12 Average displacement in E- Glass fiber

30

CHAPTER –6

CONCLUSION

In this paper, the stress analysis of disk brakes in severe braking conditions has

been performed. ANSYS software is applied to the stress problem with frictional heat

generation. To obtain the behaviors appearing in the disc brake, the change in pressure and

temperature were calculated to analyze the disc brake under severe conditions. Also, the fully

implicit scheme is used to improve the accuracy of computations in the stress analysis.

Through the axis symmetric disk brake model, the stress phenomenon on each of the

friction surfaces between the contacting bodies has been investigated. The effects of the

material properties on the contact ratio of friction surfaces are examined and the larger

influential properties are found to be the thermal expansion coefficient and the elastic

modulus. Based on these numerical results, the stress behaviors of the glass fiber

composite disk brakes are also investigated along with metal matrix composites(Alumina). It

is observed that the alumina based brakes can provide better brake performance than the

isotropic ones because of uniform and mild pressure distributions.

The present study can provide a useful design tool and improve the brake

performance of disk brake system. From Table 6.1 we can say that all the values obtained from

the analysis are less than their allowable values. Hence the brake disk design is safe based on

the strength and rigidity criteria. It is concluded that the Alumina disc brake is better than the

other compared materials for the present day applications. .

31

CI SS AL E-GLASS0.00E+000

1.00E+008

2.00E+008

3.00E+008

4.00E+008

5.00E+008

6.00E+008

7.00E+008

8.00E+008

Stre

ss v

alue

Materials

Stress

Figure 6.1 Graph - Comparison of the stress

CI SS AL E-GLASS0.00000

0.00005

0.00010

0.00015

0.00020

0.00025

0.00030

Stra

in v

alue

Materials

Strain value

Figure 6.2 Graph - Comparison for Strain

32

CI SS AL E-GLASS0.00

0.02

0.04

0.06

0.08

Dis

plac

emen

t

Materials

Displacement

Figure 6.3 Graph - Comparison for displacement

Table 6.1 Comparison of the result

MaterialVon-mises stress Elastic strain

DeflectionMin Max Min Max

Cast iron 0.879e7 0.822e9 0.12e-3 0.3e-3 0.07711

Stainless steel 0.617e7 0.480e9 0.102e-3 0.271e-3 0.0698

Alumina 0.49e7 0.27e9 0.820e-4 0.2e-3 0.0544

E-glass fiber 0.137e8 0.65e9 0.137e-3 0.32e-3 0.0594

33

SCOPE FOR THE FURTHER STUDY

In the present investigation of thermal analysis of disk brake, a simplified disk brake

without any vents, with only ambient air-cooling is analyzed by FEM package ANSYS.

As future work, a complicated model of ventilated disk brake can be taken and there

by forced convection to be considered in the analysis. The analysis still becomes

complicated by considering variable thermal conductivity, variable specific heat and non

uniform deceleration of vehicle. This can be considered for the future work.

34

REFRENCES

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5. WANG, H. -C. AND BANERJEE, P. K.. Generalized Axis symmetric

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6. FLOQUET, A. AND DUBOURG, M.-C. Non axis symmetric effects for three

dimensional Analyses of a Brake, ASME J. Tribology, vol. 116, page 401-407, (1994).

7. BURTON, R. A. Thermal Deformation in Frictionally Heated Contact, Wear, vol.

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8. ANDERSON, A. E. AND KNAPP, R. A. Hot Spotting in Automotive Friction

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